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Full text of "Text Book Of Mechanical Engineering"

Simple Machines.

481

and they can all be placed under two divisions  levers and
inclined planes. There is always a point P where the energy
enters, and a point W where it is removed,"* and the Principle
of Work states that

Work put in at P = work taken out at W
neglecting resistances.    But as work = force x distance,

where d = distance travelled by P, and D that travelled by W.

This is the underlying principle, and our investigations on
machines are for the purpose of finding the comparison of the
distances or speeds at P and W, for by inversion we shall obtain
the relation of the forces W and P. The first is the ratio of
virtual velocities and the second is mechanical advantage. Then,
generally,

veLP       force W

-  = - - ~~
vel. W      force P

.

= Mech. Adv. -=*
P

Mech. Adv.

The Lever is shewn under various forms in Fig. 436.    By
moments :

Pa - WA        and     Mech. Adv. - ? - | ^ ****** Z>

P      A         p. 763.)

The Wheel  and Axle, Fig. 437, is reckoned similarly,
and its

a         handle

A "" barrel rad.

A train cf gearing in Fig. 438 consists of two pairs of wheels,
a handle, and a barrel. The advantage of the first pair would

be - : of the second pair  : and of the wheel and axle -.    So
A                               Aj                                           A2

the total

Mech. Adv. -=r- = ~ x -A- x 
P      A      Aj      A2

* The old letters P and W being retained, are, meant to represent the forces
and also the points of application. Rankine called them effort and resistance
respectively. Note that fractional and other losses are entirely-neglected on
pp. 481-4 and Theoretical mechanical advantage is therefore the result.

(Sup, 954- )